Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
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The Geometry of Exponential Families. Calculus on Manifolds. Statistical Manifolds. Connections. Curvature. Information Metrices and Statistical Divergences. Asymptotics. Bundles and Tensors. Higher Order Geometry. References. Index.
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Descrizione libro Chapman and Hall/CRC, 1993. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria F9-9780412398605
Descrizione libro 1993. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria VT-9780412398605
Descrizione libro Chapman and Hall/CRC, 2017. Hardback. Condizione libro: NEW. 9780412398605 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Print on Demand title, produced to the highest standard, and there would be a delay in dispatch of around 10 working days. Codice libro della libreria HTANDREE0246886
Descrizione libro Chapman and Hall/CRC, 1993. Hardcover. Condizione libro: New. book. Codice libro della libreria 0412398605
Descrizione libro Chapman & Hall, 1993. Hardcover. Condizione libro: Brand New. 1st edition. 288 pages. 9.00x5.50x0.75 inches. In Stock. Codice libro della libreria __0412398605
Descrizione libro Chapman and Hall/CRC, 1993. Hardcover. Condizione libro: New. 1. Codice libro della libreria DADAX0412398605
Descrizione libro 1993. Hardcover. Condizione libro: New. 1st. 154mm x 21mm x 240mm. Hardcover. Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the applica.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 292 pages. 0.540. Codice libro della libreria 9780412398605